Sit down and get ready for a heartbreak, but ArchiCAD's Rendering Engine doesn't render reflections because it lacks raytracing or radiosity.
To achieve mirror and chrome reflections with ArchiCAD models, here are your options. They all cost a piece:
1: AV Works - plug-in for ArchiCAD - cheap and okay.
2: Artlantis Render - Receives model from ArchiCAD - allows for camera changes, material changes and lighting but no edit of the model.
3: Archilumos - just getting started but is a sophisticated plug-in with radiosity rendering... and fast.
4: Almost any other Rendering Application where ArchiCAD models are exported - the trick is to successfully link ArchiCAD material definitions with the more sophisticated materials found in, say, Cinema 4D or Electric Image.